The ProjectionCAD Package

Latest Code

The latest version of the code is available here. To use it you need Maple and a copy of the RegularChains Library (which is distributed with latter versions of Maple). The code has been tested with Maple 18 and the RC Library it ships with. It is likely to also work with Maple 16, 17 and 2015.

Also available is a Maple worksheet introducing the full functionality of the code and a pdf printout of the worksheet.

Brief Description

ProjectionCAD is a Maple package developed by the team at the University of Bath. The primary developer is Dr. Matthew England and feedback and bug reports should be reported to him at M.England@bath.ac.uk

The package produces CADs via the traditional approach of projection and lifting. This is in contrast to the built-in Maple CAD command which uses the theory of Regular Chains. However, ProjectionCAD does make use of many RegularChains commands and can give output in the same format.

The code can produce CADs which are: sign-invariant, order-invariant, invariant with respect to equational constraint and truth-table invariant. There are also commands for choosing the best problem formulation for the CAD algorithms. [England13a] describes how this package is the only implementation of McCallum's delineating polynomials and the only package to offer order-invariant output. [England13b] describes how the equational constraints commands offer not only improved projection but also improved lifting, as well as extensions to the original TTICAD algorithm.

Publications

The following publication describes the ProjectionCAD package to date (up to Version 3) and should be the main reference for the package.

  • [EWBD14]
    M. England, D. Wilson, R. Bradford and J.H. Davenport.
    Using the Regular Chains Library to build cylindrical algebraic decompositions by projecting and lifting.
    In: H. Hong and C. Yap, eds. Mathematical Software - ICMS 2014, pp. 458-465. (Lecture Notes in Computer Science, 8592). Springer Berlin Heidelberg, 2014.
    Publication website. Digital Object Identifier: doi:10.1007/978-3-662-44199-2_69
    Final version pdf.
    Preprint arXiv:1405.6090 or University repository.

The three releases of ProjectionCAD have all been accomanied by their own technical reports: